Electrical impedance tomography (EIT), in which a volume is probed non-invasively by injecting currents (or magnetic fields) and measuring the electrical potential or magnetic fields at the periphery, has been reported as being useful for physiological imaging for some three decades.
Its applicability in industrial situations, in which it is called “process tomography”, was recognized in the early 1980's, leading to a considerable investment in research into hardware, software, and reconstruction algorithms. More recently, there has been a growing interest in obtaining material contrast in the images by discriminating on the basis of the frequency response of impedance; this is electrical impedance spectroscopy (EIS). The combination of the two methods is generally called electrical impedance tomography spectroscopy (EITS).
In the standard implementation of EIT, the complex impedance is measured in terms of resistance and capacitance. A ring of electrodes is placed around the volume to be imaged; a current is injected through a pair of the electrodes, and the resulting electrical potentials measured at all or many of the other of the multiple electrodes employed. The signals are separated into a resistive and a capacitive signal, either by measuring the complex impedance directly, or by using separate ohmic and capacitive electrodes.
If the frequency of the injected current is swept through a range, or stepped through a set of fixed frequencies, the spectral response may also be obtained. For this purpose excitation current is switched sequentially to different pairs of electrodes, and a series of data sets acquired sequentially. When all the desired combinations have been measured, a reconstruction algorithm is used to produce an approximation of the distribution of material within the image plane, based on its impedance (in EIT) or impedance spectrum (in EITS). The reconstruction of EITS images is an area of active research, and many different methods are available (See McEwan, A., Romsauerova, A., Yerworth, R., Horesh, L., Bayford, R., & Holder, D. (2006). Design and calibration of a compact multi-frequency EIT system for acute stroke imaging, Physiol. Meas., 27, S199-S210).
There are a number of standard patterns of excitation and measurement in EITS. The most commonplace is that adjacent pairs of electrodes are used to inject current, and potentials are measured at the other electrodes. Regardless of the pattern used, a single frame of EIT data requires a great many measurements (the adjacent-pair method requires k=n×(n−1) measurements for n electrodes); and this number must be multiplied by the number of frequency points required.
Taking a frame of EIT data using sequential measurements (so-called time-division multiplexed or TDM measurements) is slow, so that frame rates in excess of 100 frames/second are extremely difficult to achieve. Whilst optimization of the TDM process to a very high degree is reported to have achieved frame rates of up to 1000 frames/second, most laboratory and commercial systems operate at orders of magnitude slower than this. EITS systems are slower still, with frame rates of 13 seconds/frame being generally achievable with a frequency range of 20 Hz-128 kHz in present day systems.
A basic constraint in EITS frame rate is imposed by the lower limit of spectral bandwidth; for example, if the impedance at 20 Hz is required, the frame rate per second will be limited to 20/k, where k is the number of sequential measurements required per frame; and even this limit implies sampling only a single cycle of the lowest frequency per measurement, which is somewhat difficult to achieve in practice. Use in the past has thus been limited, for example to EIT imaging of fast electrical and slow blood flow related changes during functional activity and epilepsy. These applications have traditionally used time-division multiplexing (TDM) of a single current source to pairs of electrodes over say 258 electrode combinations.
A method which presents itself for increasing the frame rate is to simultaneously inject currents which are modulated to be mathematically orthogonal, so that their contributions to the potential at any electrode can be separated by demodulation. For example, if a current of frequency f1 is injected at one pair of electrodes, and a current of frequency f2 at a second pair, then the potential across a third pair of electrodes can be separated into a component due to f1 and a component due to f2 by synchronously demodulating with those frequencies. The complex components of impedance can be extracted by in-phase and quadrature synchronous demodulation. The process is referred to as frequency-division multiplexed (FDM EIT).
A number of problems are encountered in FDM EIT as a consequence of accommodating simultaneous current injection and voltage measurement on the same electrode. If the current and voltage form part of the same impedance calculation, this comprises a two-terminal impedance measurement; whereas it is generally considered that a four-terminal measurement is required to avoid the problem of inadvertently including the contact or terminal resistance in the specimen resistance. If the current and voltage form part of a separate calculation, then this problem is avoided.
A second issue is that the current through any terminal must be a sum of orthogonal component currents, and equal and opposite components must flow through some other terminal. Ensuring that the net current due to each component is zero is electronically complicated, and has not been attempted in any of the FDM EIT systems known to applicant. These systems have generally avoided these problems by using separate sets of current injection and voltage measurement electrodes, although this has the disadvantage that twice the number of electrodes are required to obtain the same resolution.
Zimmerman et al in US published patent application US2004/201380 propose the use of orthogonal signals, either discrete sine waves or coded binary signals, as a way to use plural excitation electrodes simultaneously. However, their main application is in geophysics in which the focus is on detecting aqueous or metallic objects in a composite earth body which have a constant conductivity difference relative to the background. As a result of this their intended use of the system is apparently confined to within a small frequency range, their example of 10 Hz-19.9 Hz being illustrative of this.